def test_uhf_energy_same_as_rhf(atomzs, dist, energy_true, variational):
# test to see if uhf energy gets the same energy as rhf for non-polarized systems
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype) * dist
mol = Mol((atomzs, poss), basis=basis, dtype=dtype)
qc = HF(mol, restricted=False, variational=variational).run()
ene = qc.energy()
assert torch.allclose(ene, ene * 0 + energy_true, rtol=1e-8)
def test_uhf_energy_atoms(atomz, spin, energy_true, variational):
# check the energy of atoms with non-0 spins
torch.manual_seed(123)
poss = torch.tensor([[0.0, 0.0, 0.0]], dtype=dtype)
mol = Mol(([atomz], poss), basis=basis, dtype=dtype, spin=spin)
qc = HF(mol, restricted=False, variational=variational).run()
ene = qc.energy()
assert torch.allclose(ene, ene * 0 + energy_true, atol=0.0, rtol=1e-7)
def get_energy(atomz, with_ii=True):
atomzs = [atomz, atomz]
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype)
mol = Mol((atomzs, poss), basis=basis, spin=0, dtype=dtype)
qc = HF(mol, restricted=True).run()
ene = qc.energy()
if with_ii:
ene = ene - mol.get_nuclei_energy()
return ene
def test_uhf_energy_mols(atomzs, dist, spin, energy_true, variational):
# check the energy of molecules with non-0 spins
# NOTE: O2 iteration gets into excited state (probably)
torch.manual_seed(123)
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype) * dist
mol = Mol((atomzs, poss), basis=basis, dtype=dtype, spin=spin)
qc = HF(mol, restricted=False, variational=variational).run()
ene = qc.energy()
assert torch.allclose(ene, ene * 0 + energy_true, rtol=1e-8, atol=0.0)
def _test_hf_mols():
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]],
dtype=dtype) * dist
poss = poss.requires_grad_()
mol = Mol((atomzs, poss), basis="6-311++G**", dtype=dtype, spin=spin)
qc = HF(mol).run()
ene = qc.energy()
# see if grad and backward create memleak
grads = torch.autograd.grad(ene, (poss, ), create_graph=True)
ene.backward() # no create_graph here because of known pytorch's leak
def test_rhf_energy_overcomplete(atomzs, dist, energy_true, variational):
# test to see if the energy calculated by DQC agrees with PySCF with
# overcomplete basis
torch.manual_seed(123)
# double the basis to make it overcomplete
basis0 = loadbasis(f"{atomzs[0]}:{basis}") * 2
basis1 = loadbasis(f"{atomzs[1]}:{basis}") * 2
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype) * dist
# orthogonalize_basis = True to handle overcomplete
mol = Mol((atomzs, poss), basis=[basis0, basis1], dtype=dtype, orthogonalize_basis=True)
qc = HF(mol, restricted=True, variational=variational).run()
ene = qc.energy()
assert torch.allclose(ene, ene * 0 + energy_true, rtol=1e-7)
def test_cgto_dm2grid(system1):
# test the function aodm2dens in hamilton cgto
# using converged HF system to make it independent of the definition of dm
# in DQC and PySCF
torch.manual_seed(123)
qc = HF(system1).run()
dm1 = qc.aodm()
hamilton1 = system1.get_hamiltonian()
nao = hamilton1.nao
nb = 2
# prepare the density matrix
dm = torch.zeros((nb, nao, nao), dtype=dtype)
dm[1] = dm1
# prepare the grids
# 0th row: middle point between two atoms
# 1st row: position of the first atom
# 2nd row: position of the second atom
grids = torch.tensor([
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.4],
[0.0, 0.0, 0.8],
[0.0, 0.0, -0.4],
[0.0, 0.0, -0.8]
], dtype=dtype).unsqueeze(1) # (ngrid, 1, ndim)
ngrid = grids.shape[0]
# # pyscf code to obtain the actual results
# from pyscf import gto, scf
# from pyscf.dft import numint
# mol = gto.M(atom="H 0 0 0.8; H 0 0 -0.8", basis="3-21G", unit="Bohr")
# mf = scf.RHF(mol)
# ene = mf.kernel()
# dm_scf = mf.make_rdm1()
# ao = numint.eval_ao(mol, grids[:, 0, :].numpy())
# dens1 = numint.eval_rho(mol, ao, dm_scf)
# print(dens1)
# raise RuntimeError
dens = hamilton1.aodm2dens(dm, grids) # (ngrid, nb)
dens_true = torch.tensor([
[0.0, 0.0, 0.0, 0.0, 0.0],
[0.18742819, 0.23469519, 0.30250292, 0.23469519, 0.30250292],
], dtype=dens.dtype).transpose(-2, -1)
assert list(dens.shape) == [ngrid, nb]
assert torch.allclose(dens, dens_true)
def test_rhf_energy(atomzs, dist, energy_true, variational):
# test to see if the energy calculated by DQC agrees with PySCF
torch.manual_seed(123)
# only set debugging mode only in one case to save time
if atomzs == [1, 1]:
xt.set_debug_mode(True)
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype) * dist
mol = Mol((atomzs, poss), basis=basis, dtype=dtype)
qc = HF(mol, restricted=True, variational=variational).run()
ene = qc.energy()
assert torch.allclose(ene, ene * 0 + energy_true, rtol=1e-7)
if atomzs == [1, 1]:
xt.set_debug_mode(False)
def test_rhf_basis_inputs():
# test to see if the various basis inputs produce the same results
atomzs = [1, 1]
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype) * 1.0
mol0 = Mol((atomzs, poss), basis=basis, dtype=dtype)
ene0 = HF(mol0, restricted=True).run().energy()
mol1 = Mol((atomzs, poss), basis=[basis, basis], dtype=dtype)
ene1 = HF(mol1, restricted=True).run().energy()
assert torch.allclose(ene0, ene1)
mol1 = Mol((atomzs, poss), basis=loadbasis("1:" + basis), dtype=dtype)
ene1 = HF(mol1, restricted=True).run().energy()
assert torch.allclose(ene0, ene1)
mol2 = Mol((atomzs, poss), basis={"H": basis}, dtype=dtype)
ene2 = HF(mol2, restricted=True).run().energy()
assert torch.allclose(ene0, ene2)
mol2 = Mol((atomzs, poss), basis={1: basis}, dtype=dtype)
ene2 = HF(mol2, restricted=True).run().energy()
assert torch.allclose(ene0, ene2)
mol2 = Mol((atomzs, poss), basis={1: loadbasis("1:3-21G")}, dtype=dtype)
ene2 = HF(mol2, restricted=True).run().energy()
assert torch.allclose(ene0, ene2)
def h2o_qc():
# run the self-consistent HF iteration for h2o
atomzs = torch.tensor([8, 1, 1], dtype=torch.int64)
# from CCCBDB (calculated geometry for H2O)
atomposs = torch.tensor([
[0.0, 0.0, 0.2156],
[0.0, 1.4749, -0.8625],
[0.0, -1.4749, -0.8625],
], dtype=dtype).requires_grad_()
efield = torch.zeros(3, dtype=dtype).requires_grad_()
grad_efield = torch.zeros((3, 3), dtype=dtype).requires_grad_()
efields = (efield, grad_efield)
mol = Mol(moldesc=(atomzs, atomposs), basis="3-21G", dtype=dtype, efield=efields)
qc = HF(mol).run()
return qc
def get_energy(dist_tensor):
poss_tensor = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype) * dist_tensor
mol = Mol((atomzs, poss_tensor), basis=basis, dtype=dtype)
qc = HF(mol, restricted=True, variational=variational).run(
fwd_options=fwd_options, bck_options=bck_options)
return qc.energy()
def get_energy(atomzs):
poss = torch.tensor([[-0.5, 0.0, 0.0], [0.5, 0.0, 0.0]], dtype=dtype)
mol = Mol((atomzs, poss), basis=basis, spin=0, dtype=dtype)
qc = HF(mol, restricted=True).run()
ene = qc.energy() - mol.get_nuclei_energy()
return ene
def test_instability_check():
# check if is_orb_min returns False for a known excited state
atomzs = [8, 8] # O2
atomposs = torch.tensor([[-1.0, 0., 0.], [1.0, 0., 0.]], dtype=dtype)
mol = Mol(moldesc=(atomzs, atomposs), basis="3-21G", dtype=dtype, spin=2)
# known excited state of O2
dm0 = SpinParam(u=torch.tensor([[ 1.4374e-02, -6.5933e-17, -1.3556e-17, 1.1258e-17, -1.8834e-03,
2.1021e-16, -2.3638e-13, -2.6444e-12, 2.2637e-02, -4.9366e-17,
-5.9629e-02, 1.8549e-17, 5.0367e-17, -1.5571e-16, -5.6398e-12,
-6.9681e-12, -1.0048e-01, 1.2257e-15],
[-6.5933e-17, 2.3236e-02, -2.1167e-12, -5.2740e-13, -7.3181e-17,
-1.0873e-02, -8.3590e-17, 1.2056e-17, -9.3082e-17, 8.0595e-02,
3.6757e-16, 9.1094e-12, -3.9485e-13, 1.2539e-01, -9.1129e-18,
-2.8306e-17, -7.9300e-17, -1.8937e-02],
[-1.3556e-17, -2.1167e-12, 4.2572e-02, 8.2444e-04, -1.2280e-16,
1.5572e-12, -1.5306e-17, 1.7276e-16, 2.7191e-18, 6.4115e-13,
1.1101e-16, -1.9820e-01, -3.8413e-02, -1.7302e-12, -7.2395e-16,
-5.6557e-16, 1.6237e-17, 2.3304e-13],
[ 1.1258e-17, -5.2740e-13, 8.2444e-04, 3.9468e-02, 6.1344e-17,
3.8795e-13, 1.2361e-16, -6.1389e-18, 8.2929e-17, 1.5994e-13,
-1.2242e-16, -4.0719e-02, 1.9040e-01, -4.3109e-13, 2.8388e-17,
-3.7710e-16, 9.6793e-17, 5.8088e-14],
[-1.8834e-03, -7.3181e-17, -1.2280e-16, 6.1344e-17, 2.6433e-04,
-1.9302e-19, -1.0905e-13, -1.2203e-12, -1.8316e-03, -1.1234e-16,
4.4601e-03, 5.1546e-16, 4.1761e-16, -5.2628e-16, -7.2761e-12,
-8.9879e-12, 1.5410e-02, -1.5680e-16],
[ 2.1021e-16, -1.0873e-02, 1.5572e-12, 3.8795e-13, -1.9302e-19,
1.9720e-02, -4.5050e-18, 4.1017e-17, 5.5749e-17, -4.4163e-02,
-3.6973e-16, -6.9926e-12, 3.0281e-13, -3.5499e-02, 5.1310e-16,
-3.6489e-17, -2.1794e-16, 1.2650e-01],
[-2.3638e-13, -8.3590e-17, -1.5306e-17, 1.2361e-16, -1.0905e-13,
-4.5050e-18, 1.7231e-02, -1.7505e-04, -9.2770e-14, -3.9129e-16,
3.4332e-13, -4.4355e-18, 8.8915e-16, -4.0986e-16, -9.3919e-02,
9.0076e-02, 1.0851e-12, 1.3598e-16],
[-2.6444e-12, 1.2056e-17, 1.7276e-16, -6.1389e-18, -1.2203e-12,
4.1017e-17, -1.7505e-04, 1.5289e-02, -1.0377e-12, 1.2434e-17,
3.8408e-12, -1.3267e-15, -1.7575e-16, 1.1638e-16, 8.5865e-02,
8.7648e-02, 1.2149e-11, 4.9825e-17],
[ 2.2637e-02, -9.3082e-17, 2.7191e-18, 8.2929e-17, -1.8316e-03,
5.5749e-17, -9.2770e-14, -1.0377e-12, 1.0891e-01, 5.4901e-16,
-3.1041e-01, -2.1589e-16, 9.7090e-17, -2.0236e-16, 2.5871e-12,
3.1957e-12, -1.3275e-02, -3.7240e-16],
[-4.9366e-17, 8.0595e-02, 6.4115e-13, 1.5994e-13, -1.1234e-16,
-4.4163e-02, -3.9129e-16, 1.2434e-17, 5.4901e-16, 9.9128e-01,
6.4760e-16, -9.9216e-13, 4.2760e-14, -1.2043e-02, 1.5942e-16,
-1.0898e-16, 1.7759e-16, 7.3878e-03],
[-5.9629e-02, 3.6757e-16, 1.1101e-16, -1.2242e-16, 4.4601e-03,
-3.6973e-16, 3.4332e-13, 3.8408e-12, -3.1041e-01, 6.4760e-16,
8.8722e-01, -4.5809e-17, 1.7987e-16, -2.7821e-16, 2.1268e-13,
2.6265e-13, -1.1616e-02, -1.0344e-16],
[ 1.8549e-17, 9.1094e-12, -1.9820e-01, -4.0719e-02, 5.1546e-16,
-6.9926e-12, -4.4355e-18, -1.3267e-15, -2.1589e-16, -9.9216e-13,
-4.5809e-17, 9.5723e-01, 1.5197e-04, -1.8852e-12, 1.6341e-16,
1.0968e-16, -7.3105e-17, 1.1978e-12],
[ 5.0367e-17, -3.9485e-13, -3.8413e-02, 1.9040e-01, 4.1761e-16,
3.0281e-13, 8.8915e-16, -1.7575e-16, 9.7090e-17, 4.2760e-14,
1.7987e-16, 1.5197e-04, 9.6073e-01, 8.1569e-14, -4.7992e-16,
3.4136e-16, 3.3857e-17, -5.1807e-14],
[-1.5571e-16, 1.2539e-01, -1.7302e-12, -4.3109e-13, -5.2628e-16,
-3.5499e-02, -4.0986e-16, 1.1638e-16, -2.0236e-16, -1.2043e-02,
-2.7821e-16, -1.8852e-12, 8.1569e-14, 9.8251e-01, 1.5091e-16,
-1.8316e-16, -1.7641e-16, 7.2007e-03],
[-5.6398e-12, -9.1129e-18, -7.2395e-16, 2.8388e-17, -7.2761e-12,
5.1310e-16, -9.3919e-02, 8.5865e-02, 2.5871e-12, 1.5942e-16,
2.1268e-13, 1.6341e-16, -4.7992e-16, 1.5091e-16, 9.8353e-01,
9.6527e-04, -1.3954e-12, 5.5578e-17],
[-6.9681e-12, -2.8306e-17, -5.6557e-16, -3.7710e-16, -8.9879e-12,
-3.6489e-17, 9.0076e-02, 8.7648e-02, 3.1957e-12, -1.0898e-16,
2.6265e-13, 1.0968e-16, 3.4136e-16, -1.8316e-16, 9.6527e-04,
9.8395e-01, -1.7236e-12, 1.2375e-16],
[-1.0048e-01, -7.9300e-17, 1.6237e-17, 9.6793e-17, 1.5410e-02,
-2.1794e-16, 1.0851e-12, 1.2149e-11, -1.3275e-02, 1.7759e-16,
-1.1616e-02, -7.3105e-17, 3.3857e-17, -1.7641e-16, -1.3954e-12,
-1.7236e-12, 9.8924e-01, -1.2411e-16],
[ 1.2257e-15, -1.8937e-02, 2.3304e-13, 5.8088e-14, -1.5680e-16,
1.2650e-01, 1.3598e-16, 4.9825e-17, -3.7240e-16, 7.3878e-03,
-1.0344e-16, 1.1978e-12, -5.1807e-14, 7.2007e-03, 5.5578e-17,
1.2375e-16, -1.2411e-16, 9.8325e-01]], dtype=torch.float64),
d=torch.tensor([[ 2.2958e-02, 5.9133e-17, -4.3465e-17, -3.5203e-17, -5.2141e-03,
1.9909e-16, 1.6717e-14, 1.8684e-13, 3.9446e-02, 2.7848e-16,
-6.6246e-02, 1.2336e-17, -2.6465e-16, 8.6160e-16, -2.8860e-11,
-3.5653e-11, -1.2829e-01, 1.5006e-15],
[ 5.9133e-17, 4.6415e-03, -1.3965e-10, -3.4794e-11, -2.6531e-17,
-7.5184e-03, 6.8007e-17, -1.8251e-17, 1.2508e-16, 4.6059e-02,
-5.7129e-18, 6.4528e-10, -2.7957e-11, -7.4002e-03, -7.1789e-16,
5.1820e-16, -9.0260e-16, -4.8860e-02],
[-4.3465e-17, -1.3965e-10, 4.3859e-02, 1.0928e-02, -6.8315e-17,
6.4583e-11, 1.4620e-17, 1.7630e-16, -1.1049e-16, -2.1608e-10,
2.5101e-16, -2.0430e-01, 8.8512e-03, -7.6096e-10, -7.9051e-16,
-5.0478e-16, 1.2440e-16, -8.9813e-11],
[-3.5203e-17, -3.4794e-11, 1.0928e-02, 2.7228e-03, -1.0420e-17,
1.6091e-11, 3.7273e-17, 1.7772e-17, -2.7800e-17, -5.3837e-11,
5.6712e-18, -5.0902e-02, 2.2053e-03, -1.8960e-10, -7.8317e-16,
8.0795e-17, 2.4562e-16, -2.2377e-11],
[-5.2141e-03, -2.6531e-17, -6.8315e-17, -1.0420e-17, 1.2314e-03,
-5.6992e-18, -1.4157e-13, -1.5837e-12, -7.1148e-03, 7.0004e-17,
9.4083e-03, 3.5543e-16, 4.2740e-17, -2.7677e-16, -2.1264e-12,
-2.6263e-12, 3.2613e-02, 1.1833e-18],
[ 1.9909e-16, -7.5184e-03, 6.4583e-11, 1.6091e-11, -5.6992e-18,
1.6029e-02, -2.4000e-17, 2.0307e-17, 1.2229e-16, -3.2365e-02,
-2.4677e-16, -2.8977e-10, 1.2554e-11, -5.3257e-03, 2.8397e-16,
-1.7180e-16, -8.3203e-17, 1.2099e-01],
[ 1.6717e-14, 6.8007e-17, 1.4620e-17, 3.7273e-17, -1.4157e-13,
-2.4000e-17, 3.7952e-03, 7.4301e-04, -4.3281e-13, 4.4101e-16,
-1.6173e-12, -4.2060e-17, 2.1463e-16, 2.1636e-16, -4.1059e-02,
4.5765e-02, -2.8999e-12, 1.0801e-16],
[ 1.8684e-13, -1.8251e-17, 1.7630e-16, 1.7772e-17, -1.5837e-12,
2.0307e-17, 7.4301e-04, 1.2040e-02, -4.8418e-12, -1.2562e-16,
-1.8091e-11, -1.2667e-15, -4.7435e-17, -1.7249e-16, 7.2754e-02,
8.1250e-02, -3.2434e-11, 8.1554e-17],
[ 3.9446e-02, 1.2508e-16, -1.1049e-16, -2.7800e-17, -7.1148e-03,
1.2229e-16, -4.3281e-13, -4.8418e-12, 1.3971e-01, 1.1579e-15,
-3.3375e-01, -4.4814e-17, -5.2377e-16, 1.4905e-15, -7.4596e-11,
-9.2152e-11, -8.4825e-02, 5.5948e-16],
[ 2.7848e-16, 4.6059e-02, -2.1608e-10, -5.3837e-11, 7.0004e-17,
-3.2365e-02, 4.4101e-16, -1.2562e-16, 1.1579e-15, 9.2048e-01,
-1.0153e-16, 9.8356e-10, -4.2613e-11, -2.6337e-01, -1.3755e-15,
6.0548e-16, -1.5088e-15, -2.5713e-02],
[-6.6246e-02, -5.7129e-18, 2.5101e-16, 5.6712e-18, 9.4083e-03,
-2.4677e-16, -1.6173e-12, -1.8091e-11, -3.3375e-01, -1.0153e-16,
8.6354e-01, 9.1119e-17, 9.7805e-16, -3.0709e-15, -3.0487e-11,
-3.7662e-11, -4.4392e-02, -2.2345e-16],
[ 1.2336e-17, 6.4528e-10, -2.0430e-01, -5.0902e-02, 3.5543e-16,
-2.8977e-10, -4.2060e-17, -1.2667e-15, -4.4814e-17, 9.8356e-10,
9.1119e-17, 9.5163e-01, -4.1229e-02, 3.5411e-09, 3.4000e-16,
-7.3179e-17, 4.4148e-17, 5.0171e-10],
[-2.6465e-16, -2.7957e-11, 8.8512e-03, 2.2053e-03, 4.2740e-17,
1.2554e-11, 2.1463e-16, -4.7435e-17, -5.2377e-16, -4.2613e-11,
9.7805e-16, -4.1229e-02, 1.7862e-03, -1.5342e-10, -3.2950e-15,
1.6944e-15, 1.3384e-15, -2.1736e-11],
[ 8.6160e-16, -7.4002e-03, -7.6096e-10, -1.8960e-10, -2.7677e-16,
-5.3257e-03, 2.1636e-16, -1.7249e-16, 1.4905e-15, -2.6337e-01,
-3.0709e-15, 3.5411e-09, -1.5342e-10, 8.9643e-02, -5.2073e-15,
2.4346e-15, -5.8143e-15, -1.1027e-01],
[-2.8860e-11, -7.1789e-16, -7.9051e-16, -7.8317e-16, -2.1264e-12,
2.8397e-16, -4.1059e-02, 7.2754e-02, -7.4596e-11, -1.3755e-15,
-3.0487e-11, 3.4000e-16, -3.2950e-15, -5.2073e-15, 9.9295e-01,
-4.0971e-03, -9.4472e-12, -6.9572e-16],
[-3.5653e-11, 5.1820e-16, -5.0478e-16, 8.0795e-17, -2.6263e-12,
-1.7180e-16, 4.5765e-02, 8.1250e-02, -9.2152e-11, 6.0548e-16,
-3.7662e-11, -7.3179e-17, 1.6944e-15, 2.4346e-15, -4.0971e-03,
9.9121e-01, -1.1671e-11, 5.1711e-16],
[-1.2829e-01, -9.0260e-16, 1.2440e-16, 2.4562e-16, 3.2613e-02,
-8.3203e-17, -2.8999e-12, -3.2434e-11, -8.4825e-02, -1.5088e-15,
-4.4392e-02, 4.4148e-17, 1.3384e-15, -5.8143e-15, -9.4472e-12,
-1.1671e-11, 9.7256e-01, -8.6388e-16],
[ 1.5006e-15, -4.8860e-02, -8.9813e-11, -2.2377e-11, 1.1833e-18,
1.2099e-01, 1.0801e-16, 8.1554e-17, 5.5948e-16, -2.5713e-02,
-2.2345e-16, 5.0171e-10, -2.1736e-11, -1.1027e-01, -6.9572e-16,
5.1711e-16, -8.6388e-16, 9.6920e-01]], dtype=torch.float64))
qc = HF(mol).run(dm0=dm0)
ene = qc.energy()
assert not is_orb_min(qc)
# known ground state of O2
dm1 = SpinParam(u=torch.tensor([[ 2.0683e-02, -1.4420e-16, 1.8209e-17, -8.9218e-18, -1.1292e-03,
2.4994e-16, 1.3424e-17, -1.3778e-17, 3.1936e-02, -2.0260e-16,
-6.6341e-02, 5.2691e-17, -3.3777e-17, -6.2702e-16, -1.9655e-17,
-1.3381e-15, -1.2179e-01, 1.1911e-15],
[-1.4420e-16, 2.5205e-02, 1.5440e-18, -1.5470e-18, -1.2490e-16,
-1.1032e-02, -4.4534e-17, -4.0071e-17, -1.5877e-16, 8.2001e-02,
3.1857e-16, 3.3331e-16, -2.5398e-16, 1.3203e-01, -1.0306e-16,
1.1040e-17, -7.2944e-17, -1.7112e-02],
[ 1.8209e-17, 1.5440e-18, 3.6441e-02, 1.0879e-13, -1.1019e-16,
-6.7960e-17, 2.3446e-17, 1.4381e-16, -1.3948e-17, 6.9656e-17,
6.2990e-17, -1.8362e-01, -3.7391e-02, 4.0401e-16, -7.8922e-16,
-5.2022e-16, -2.4977e-16, -2.3482e-17],
[-8.9218e-18, -1.5470e-18, 1.0879e-13, 3.6441e-02, 5.4484e-17,
-1.0500e-16, 8.8368e-17, -3.8825e-17, 3.4381e-17, 2.4618e-16,
-1.2742e-16, -3.7391e-02, 1.8362e-01, 2.4770e-16, -2.9739e-16,
-2.9106e-16, 9.1167e-17, 5.5659e-17],
[-1.1292e-03, -1.2490e-16, -1.1019e-16, 5.4484e-17, 7.1554e-05,
1.1112e-17, 2.0896e-17, -8.7962e-18, -8.9524e-04, -1.6020e-16,
1.0596e-03, 4.8917e-16, 3.8244e-16, -8.4877e-16, -1.6487e-16,
1.5251e-16, 8.2674e-03, -2.0908e-16],
[ 2.4994e-16, -1.1032e-02, -6.7960e-17, -1.0500e-16, 1.1112e-17,
1.9013e-02, -3.8712e-18, -2.4730e-18, 1.3092e-16, -4.3091e-02,
-3.6917e-16, 3.2346e-16, -3.8502e-16, -3.7068e-02, 2.5626e-17,
-2.1922e-16, -3.1125e-16, 1.2369e-01],
[ 1.3424e-17, -4.4534e-17, 2.3446e-17, 8.8368e-17, 2.0896e-17,
-3.8712e-18, 1.7462e-02, -1.4887e-11, 4.7461e-18, -8.8927e-17,
-4.0357e-17, -1.1873e-17, 5.0543e-16, -3.6232e-16, -9.4065e-02,
9.1151e-02, -1.0645e-15, 1.8543e-17],
[-1.3778e-17, -4.0071e-17, 1.4381e-16, -3.8825e-17, -8.7962e-18,
-2.4730e-18, -1.4887e-11, 1.7462e-02, -1.2512e-17, -1.1642e-16,
5.8123e-17, -1.3728e-15, -2.0690e-16, -1.4420e-16, 9.1151e-02,
9.4065e-02, -9.7118e-16, 4.9315e-17],
[ 3.1936e-02, -1.5877e-16, -1.3948e-17, 3.4381e-17, -8.9524e-04,
1.3092e-16, 4.7461e-18, -1.2512e-17, 1.2198e-01, 5.5052e-16,
-3.2192e-01, 7.7566e-18, -6.8423e-17, -6.6652e-16, 1.3687e-16,
-5.6171e-16, -4.9446e-02, -1.5290e-16],
[-2.0260e-16, 8.2001e-02, 6.9656e-17, 2.4618e-16, -1.6020e-16,
-4.3091e-02, -8.8927e-17, -1.1642e-16, 5.5052e-16, 9.9113e-01,
6.4477e-16, -1.2044e-16, -2.2427e-16, -1.2837e-02, 1.0462e-16,
-6.5168e-17, 8.9549e-17, 6.9992e-03],
[-6.6341e-02, 3.1857e-16, 6.2990e-17, -1.2742e-16, 1.0596e-03,
-3.6917e-16, -4.0357e-17, 5.8123e-17, -3.2192e-01, 6.4477e-16,
8.7574e-01, 9.2656e-17, 1.0997e-16, -4.7293e-16, 1.4328e-17,
-2.7222e-16, -2.8003e-02, -4.2238e-17],
[ 5.2691e-17, 3.3331e-16, -1.8362e-01, -3.7391e-02, 4.8917e-16,
3.2346e-16, -1.1873e-17, -1.3728e-15, 7.7566e-18, -1.2044e-16,
9.2656e-17, 9.6356e-01, 1.9387e-14, -1.1383e-16, -3.7055e-16,
2.4158e-16, -8.2073e-17, -9.3030e-17],
[-3.3777e-17, -2.5398e-16, -3.7391e-02, 1.8362e-01, 3.8244e-16,
-3.8502e-16, 5.0543e-16, -2.0690e-16, -6.8423e-17, -2.2427e-16,
1.0997e-16, 1.9387e-14, 9.6356e-01, -1.2755e-16, -4.3096e-16,
2.4102e-16, -3.6390e-17, 9.8892e-17],
[-6.2702e-16, 1.3203e-01, 4.0401e-16, 2.4770e-16, -8.4877e-16,
-3.7068e-02, -3.6232e-16, -1.4420e-16, -6.6652e-16, -1.2837e-02,
-4.7293e-16, -1.1383e-16, -1.2755e-16, 9.8060e-01, 5.0343e-17,
3.6493e-17, -2.1165e-16, 7.1881e-03],
[-1.9655e-17, -1.0306e-16, -7.8922e-16, -2.9739e-16, -1.6487e-16,
2.5626e-17, -9.4065e-02, 9.1151e-02, 1.3687e-16, 1.0462e-16,
1.4328e-17, -3.7055e-16, -4.3096e-16, 5.0343e-17, 9.8254e-01,
8.2092e-11, -1.4172e-18, 2.2854e-17],
[-1.3381e-15, 1.1040e-17, -5.2022e-16, -2.9106e-16, 1.5251e-16,
-2.1922e-16, 9.1151e-02, 9.4065e-02, -5.6171e-16, -6.5168e-17,
-2.7222e-16, 2.4158e-16, 2.4102e-16, 3.6493e-17, 8.2092e-11,
9.8254e-01, 4.9448e-18, 9.8734e-17],
[-1.2179e-01, -7.2944e-17, -2.4977e-16, 9.1167e-17, 8.2674e-03,
-3.1125e-16, -1.0645e-15, -9.7118e-16, -4.9446e-02, 8.9549e-17,
-2.8003e-02, -8.2073e-17, -3.6390e-17, -2.1165e-16, -1.4172e-18,
4.9448e-18, 9.8153e-01, -1.4542e-16],
[ 1.1911e-15, -1.7112e-02, -2.3482e-17, 5.5659e-17, -2.0908e-16,
1.2369e-01, 1.8543e-17, 4.9315e-17, -1.5290e-16, 6.9992e-03,
-4.2238e-17, -9.3030e-17, 9.8892e-17, 7.1881e-03, 2.2854e-17,
9.8734e-17, -1.4542e-16, 9.8405e-01]], dtype=torch.float64),
d=torch.tensor([[ 1.2641e-02, -1.5358e-16, 4.7752e-17, -8.9111e-18, -4.4876e-03,
2.2773e-16, 6.1698e-18, -7.4570e-18, 2.0856e-02, -6.6447e-17,
-5.7084e-02, -4.3042e-17, -5.2418e-17, -4.8881e-16, -1.3178e-17,
-1.0353e-15, -9.3633e-02, 1.2411e-15],
[-1.5358e-16, 3.0229e-02, 6.8437e-17, 3.5949e-17, -1.0507e-16,
-1.5192e-02, -1.7095e-17, -2.0281e-17, -2.3740e-16, 8.8960e-02,
5.2239e-16, 2.5002e-17, -8.2051e-17, 1.4194e-01, 1.1475e-16,
1.5330e-17, -3.2950e-17, -3.1999e-02],
[ 4.7752e-17, 6.8437e-17, 7.0466e-31, 2.7196e-31, -2.0268e-17,
-3.0557e-17, 6.9564e-18, -2.8971e-17, -1.2805e-17, 1.5775e-16,
5.3677e-17, 8.9575e-31, 3.5820e-31, 3.5525e-16, -4.2190e-16,
-2.6774e-16, -5.3815e-16, -4.5207e-17],
[-8.9111e-18, 3.5949e-17, 2.7196e-31, 3.5707e-31, 4.3021e-18,
-1.4450e-17, 8.7953e-18, -3.0556e-17, 1.6753e-17, 1.8210e-16,
-5.2250e-17, 9.0062e-31, 5.3400e-31, 1.3106e-16, -4.6254e-16,
-2.6536e-16, 1.2935e-16, 4.9788e-18],
[-4.4876e-03, -1.0507e-16, -2.0268e-17, 4.3021e-18, 1.6888e-03,
-6.6376e-18, 1.3986e-18, 3.8055e-18, -4.7627e-03, -4.8232e-16,
1.2498e-02, 1.2663e-17, 1.4987e-17, -5.3503e-16, -2.2757e-17,
4.8352e-16, 3.8560e-02, -3.3090e-16],
[ 2.2773e-16, -1.5192e-02, -3.0557e-17, -1.4450e-17, -6.6376e-18,
1.9762e-02, 1.6945e-17, 2.4527e-17, 1.1483e-16, -4.5236e-02,
-3.5267e-16, -2.8982e-18, 4.2041e-17, -4.5713e-02, -8.0265e-17,
1.0546e-18, -2.5558e-16, 1.2249e-01],
[ 6.1698e-18, -1.7095e-17, 6.9564e-18, 8.7953e-18, 1.3986e-18,
1.6945e-17, 3.5428e-03, 4.3824e-11, 1.0206e-17, -2.4135e-17,
-2.5997e-17, -9.4414e-18, 9.8201e-17, -6.4590e-17, -4.2669e-02,
4.1347e-02, -4.9636e-16, 7.9868e-17],
[-7.4570e-18, -2.0281e-17, -2.8971e-17, -3.0556e-17, 3.8055e-18,
2.4527e-17, 4.3824e-11, 3.5428e-03, -1.7468e-17, -1.2992e-16,
4.3756e-17, -1.0961e-16, -4.9473e-17, -4.8268e-17, 4.1347e-02,
4.2669e-02, -4.2779e-16, 1.5287e-16],
[ 2.0856e-02, -2.3740e-16, -1.2805e-17, 1.6753e-17, -4.7627e-03,
1.1483e-16, 1.0206e-17, -1.7468e-17, 1.0739e-01, 3.0990e-16,
-3.0878e-01, -1.4332e-16, -1.8655e-16, -6.0195e-16, -1.9554e-17,
-1.0795e-16, -7.5289e-03, -1.6864e-16],
[-6.6447e-17, 8.8960e-02, 1.5775e-16, 1.8210e-16, -4.8232e-16,
-4.5236e-02, -2.4135e-17, -1.2992e-16, 3.0990e-16, 9.8962e-01,
6.2003e-16, -4.3189e-16, -5.5535e-16, -1.5301e-02, 1.3215e-16,
-6.0640e-17, 9.2815e-17, 8.7875e-03],
[-5.7084e-02, 5.2239e-16, 5.3677e-17, -5.2250e-17, 1.2498e-02,
-3.5267e-16, -2.5997e-17, 4.3756e-17, -3.0878e-01, 6.2003e-16,
8.8879e-01, 4.0697e-16, 5.3094e-16, -4.3659e-16, -2.9932e-17,
-6.8804e-17, -9.2814e-03, -2.3331e-17],
[-4.3042e-17, 2.5002e-17, 8.9575e-31, 9.0062e-31, 1.2663e-17,
-2.8982e-18, -9.4414e-18, -1.0961e-16, -1.4332e-16, -4.3189e-16,
4.0697e-16, 4.0132e-30, 1.6971e-30, 4.3752e-16, -1.1655e-15,
-1.4303e-15, 1.7323e-16, -1.6309e-17],
[-5.2418e-17, -8.2051e-17, 3.5820e-31, 5.3400e-31, 1.4987e-17,
4.2041e-17, 9.8201e-17, -4.9473e-17, -1.8655e-16, -5.5535e-16,
5.3094e-16, 1.6971e-30, 4.1255e-30, -1.9731e-16, -1.7601e-15,
5.5023e-16, 1.8679e-16, 4.7534e-17],
[-4.8881e-16, 1.4194e-01, 3.5525e-16, 1.3106e-16, -5.3503e-16,
-4.5713e-02, -6.4590e-17, -4.8268e-17, -6.0195e-16, -1.5301e-02,
-4.3659e-16, 4.3752e-16, -1.9731e-16, 9.7688e-01, 1.6012e-16,
1.7160e-17, -1.5571e-16, 1.0700e-02],
[-1.3178e-17, 1.1475e-16, -4.2190e-16, -4.6254e-16, -2.2757e-17,
-8.0265e-17, -4.2669e-02, 4.1347e-02, -1.9554e-17, 1.3215e-16,
-2.9932e-17, -1.1655e-15, -1.7601e-15, 1.6012e-16, 9.9646e-01,
-2.4166e-10, 1.4456e-17, 2.1470e-17],
[-1.0353e-15, 1.5330e-17, -2.6774e-16, -2.6536e-16, 4.8352e-16,
1.0546e-18, 4.1347e-02, 4.2669e-02, -1.0795e-16, -6.0640e-17,
-6.8804e-17, -1.4303e-15, 5.5023e-16, 1.7160e-17, -2.4166e-10,
9.9646e-01, -6.1813e-17, 5.6203e-17],
[-9.3633e-02, -3.2950e-17, -5.3815e-16, 1.2935e-16, 3.8560e-02,
-2.5558e-16, -4.9636e-16, -4.2779e-16, -7.5289e-03, 9.2815e-17,
-9.2814e-03, 1.7323e-16, 1.8679e-16, -1.5571e-16, 1.4456e-17,
-6.1813e-17, 9.8949e-01, -1.6997e-16],
[ 1.2411e-15, -3.1999e-02, -4.5207e-17, 4.9788e-18, -3.3090e-16,
1.2249e-01, 7.9868e-17, 1.5287e-16, -1.6864e-16, 8.7875e-03,
-2.3331e-17, -1.6309e-17, 4.7534e-17, 1.0700e-02, 2.1470e-17,
5.6203e-17, -1.6997e-16, 9.8351e-01]], dtype=torch.float64))
qc = HF(mol).run(dm0=dm1)
ene = qc.energy()
assert is_orb_min(qc)
def get_energy(atomposs, efield, grad_efield):
efields = (efield, grad_efield)
mol = Mol(moldesc=(atomzs, atomposs), basis="3-21G", dtype=dtype, efield=efields)
qc = HF(mol).run()
ene = qc.energy()
return ene